Question

A tiny speck (2.0*10^-4 g) of radioactive americium-241 (molar mass 241.06 g/mol) is used in smoke detectors. How many atoms of americium-241 are there in one of these smoke detectors? (scientific notation)

Answer 1

To find the number of atoms of americium-241 in a smoke detector, we need to convert the given mass of americium-241 to moles using its molar mass.

Step-by-step explanation:

To find the number of atoms of americium-241 in a smoke detector, we need to convert the given mass of americium-241 to moles, using its molar mass. Then we can use Avogadro's number to calculate the number of atoms of americium-241.

The molar mass of americium-241 is 241.06 g/mol. We have 2.0*10^-4 g of americium-241.

To convert grams to moles, we can use the formula:

moles = mass / molar mass

So, moles of americium-241 = 2.0*10^-4 g / 241.06 g/mol

Simplifying this gives us: moles of americium-241 = 8.2994*10^-7 mol

Since there are 6.022*10^23 atoms in one mole of a substance (Avogadro's number), we can calculate the number of atoms of americium-241 in the smoke detector.

Number of atoms = moles * Avogadro's number = 8.2994*10^-7 mol * 6.022*10^23 atoms/mol

Simplifying this gives us: Number of atoms = 4.9964*10^17 atoms